Some years ago, during the late 1980's one Adam Trombley (a physicist) built, or for the sake of argument, claimed to have built a device that was COP > 50. In fact he built more than one device. The first was a closed (magnetic) circuit Homopolar Generator, and the second he describes as an oscillator. Many have claimed that Trombley is a fraud.
What he claimed was that this second device combined two different electrical frequencies in an oscillator, or oscillators, and derived from that a third frequency (heterodyne) to which the load was connected.
Some, perhaps many, have claimed that Trombley was a fraud. What few have done as far as I can find, is directly examine the devices themselves. I would here like to address the second device.
Firstly, is it possible to build a device that employs heterodynes to produce electric power? Yes, it is. wiki/Heterodyne and freepatentsonline.com.
If it is possible, by what means would such a device not require as much power to run as that which it produces? I believe Tesla's dual cored transformer offers the answer to that ((US patent no: 433,702) . Tesla devised a means to alter the EMF / CEMF phase relationship between the primary and secondary coils in that patent.
Establishing causality has always been my favourite method of discovering exactly how something does what it does, or perhaps if it could do as claimed. Discovering the 'actual' cause for the power loss in the primary winding, which coincides with the output power in a transformer was something I spent a lot of time on some time ago.
Lenz's law does not in any way claim that electrical devices cannot output more power than they consume. It simply establishes the fact that the magnetic field that arises in an electrical conductor when current 'changes' is always in opposition to that changing current. It is the electrical equivalent of inertia in the physical/mechanical world. For many years it has been utilized as a supposed proof that COP > 1 cannot ever be achieved.
Careful consideration of Lenz's law uncovers no such claim by Lenz, or his law. The claim that it proves that COP > 1 is not possible is simply a derivation. It is 'derived' from the fact that tightly coupled secondary coils in their current normal configuration cause a power loss in the primary circuit, and other examples.
Ernst Rutherford early in the twentieth century categorically stated that nuclear power was not only impossible, but that the very notion of it was 'moonshine'. He was at the time the acknowledged world expert in nuclear physics.
So, what is the 'cause' of the power loss in commonly constructed transformers?
Some might say it is the reduction of impedance in the primary circuit. Yes, there certainly is a loss of impedance, but that is a symptom of something else.
Power is required to overcome that opposing magnetic field. Some may point to that as the reason for the loss, but is it so?
If we apply Occam's Razor and thereby eliminate the secondary circuit for a moment, we have a simple inductor. Does the changing current create a loss of power in the inductor? Apparently not, and yet Lenz's law applies equally here as well. However, as 'apparent' as it is, it's not as simple as that might appear to be. In fact, it's all about time.
During the rise in current (sinusoidal in this argument), power is 'converted' (for want of a better term) into magnetic energy and therefore momentarily lost from the circuit. But, then the power in this sinusoidal current reaches it's peak and begins to subside. What happens now? The magnetic field will oppose that change too, as a reduction is also a change in current, is it not? Lenz's law applies in both directions, current going up, or down.
The current is the magnetic fields means of survival. Without it, it ceases to exist, and it will fight that change all the way to it's death by converting part of itself back into current, all the way down. If not for circuit losses (ohmic or otherwise) the current will continue to run forever as the magnetic field will keep it so. Again, this is analogous to inertia, or kinetic energy as such. Am I in error? I'm sure most, if not all of us, have observed this with inductors from time to time.
So what actually happens once we reintroduce our secondary circuit, (always with a load attached) ? Is it Lentz's Law causing the loss in power? No, it's not. That might alarm some people, and others may at this point wish to beat me with a stick, if they have no firearm at hand. However, please read on.
If we divide the AC cycle into parts, we can view (so to speak) what is actually occurring in a step by step manner. Whipping out Occam's Razor, we can slice off one half of the cycle as it is the mirror image of the other and all this phenomena applies equally in both halves. Twice per full cycle.
The current begins to rise(I get to choose the voltage sign at this point as I'm doing the writing). As Lenz observed, a magnetic field begins to rise also and takes equivalent power from the circuit as it does. The material of the core whether air or otherwise is of no consequence in this argument. Now, as there is a changing magnetic field there is also an associated A vector field (circularly polarized E field) at 90° to that magnetic field. (no math here, I'm lazy)
The secondary circuit is immersed in that A vector field, and as such a current begins to rise in reverse to the direction of current flow in the primary. This gives rise to another 'independent' magnetic field in the secondary that is of opposite sign to that of the primary's magnetic field. Here is where it gets interesting.
Remember that power is absorbed into that rising primary's magnetic field. What is going to happen when the field from the secondary cancels it out in the core (in equivalence to the load of course, which determines the amount of current that will actually flow in the secondary. And yes, I am aware of superposition. Either way the result is the same) ?
What of the electric power that went into that primary's magnetic field that just got cancelled out? How is it going to be returned on the reducing part of this half cycle? It won't be. Without going into the gory details the power/work is not returned as it is in a simple inductor. Here is our 'cause' of power loss. (Please note I am using 'power/work' as opposed to 'energy'. They're not actually interchangeable in this case. If you disagree, please explain why.)
The cancellation of that magnetic field, or portion thereof, will cause a drop in impedance in the primary circuit due to the fact that the magnetic field that impedes it's flow has been effectively reduced, so more current will run to try and re establish that magnetic field. That extra current will be equivalent to the load. A 1 to 1 relationship that closely resembles Newton's 'observations' in the physical/mechanical world. It can no longer be returned to the circuit as it is in the simple inductor.
All of the above applies in the case where there is a 180° (or thereabouts) phase relationship between the closely coupled primary and secondary magnetic circuits in transformer cores. And that is how they are made, and most will say that there is no other way. However, is it true that there is no other way? Nope, not at all. But that is a (hushed tone here) secret to most. It's not a secret to many of those here I believe.